Dispersion-Managed Optical Solitons with Higher-Order Nonlinearity

In this paper we have investigated the propagation characteristics of optical solitons in dispersion managed optical communication systems taking into account of the effect of quintic nonlinearity. Using variational formalism, several ordinary differential equations have been established for pulse parameters. These equations have been solved numerically to investigate the propagation characteristics. It has been noticed that stable periodic pulse propagation is possible over long distance. Numerical simulation has been undertaken to show that parabolic nonlinearity reduces collision distance between neighbouring pulses of the same channel.     

用变分法研究高阶色散和五阶非线性对高斯脉冲在光纤中传输特性的影响

从修正的非线性薛定谔方程出发,采用变分法,导出了在高阶色散和五阶非线性共同作用情况下高斯型脉冲参量随传输距离的演化方程组;求出了振幅与脉宽、频率与啁啾、脉宽与啁啾之间的三个重要约束关系;并进一步得出了脉宽随传输距离演化的解析解和脉冲中心位置随传输距离的演化规律;描绘了高阶色散和五阶非线性下,脉宽随传输距离演化的图形.结果表明:光纤中的高阶色散和五阶非线性都会影响高斯型脉冲各个参量的演化,但脉宽和振幅间的绝热关系并未改变.高阶色散使高斯型脉冲的脉宽展宽,五阶非线性使高斯型脉冲的脉宽压缩,它们对脉宽或初始啁啾的影响可以在一定程度上抵消,从而有可能使脉冲近似实现保形传输.     

五阶非线性作用下光纤中类明孤子运动方程的变分研究

当考虑到五阶非线性对光脉冲传输的影响时, 光纤中类明孤子的传输服从含五阶非线性修正项的非线性Schrdinger方程。利用何氏半反推法建立该类明孤子运动方程的变分形式, 然后应用何氏变分法导出该方程基态孤子解的双曲正割表达式。同时, 受何氏指数函数方法的启发, 建立了一种新的高斯表达式。一方面, 基于得到的显式表达式相关学者可进一步研究五阶非线性对光脉冲传输的影响。另一方面, 该求解过程也进一步显示了用何氏变分法求解数学物理中非线性发展方程的简洁有效性。     

Femtosecond Pulse Propagation in Optical Fibers Under Higher Order Effects: A Collective Variable Approach

Employing collective variable approach, femtosecond pulse propagation has been investigated in optical fibers using the higher order nonlinear Schrödinger equation. In order to view the pulse dynamics along the propagation distance, variation of different pulse parameters, called collective variables, such as pulse amplitude, width, chirp, pulse center and frequency has been investigated by numerically solving the set of ordinary equations obtained from collective variable approach.     

色散和非线性效应对高斯脉冲综合影响的理论分析

从光孤子传输所满足的非线性薛定谔方程出发,采用单独分析和综合分析对比,分析了影响高斯脉冲传输的色散、非线性等因素,结果表明：二阶色散参量只会影响脉冲的幅值,对脉冲形状影响不大,而输入脉冲的啁啾则是使脉冲发生形变的主要原因|在啁啾、三阶色散和五阶非线性的共同作用下,它们对脉冲都会产生较大的影响,且存在相互影响和制约作用,在某一临界值,对脉冲存在着较高的压缩增益效应和“整形”作用.从理论上提出了改善高斯光脉冲在光纤中传输特性的解决方案,这对光纤孤子通信的实践过程具有一定的理论借鉴意义.     

Asymmetrically Apodized Linearly Chirped Fiber Bragg Gratings for Efficient Pulse Compression

Abstract

A simple and stable technique of optical short pulse generation for soliton transmission based on external modulation is reviewe.By using nonlinearity of absorption characteristics of an electroabsorption modulator, ultra-short optical pulse trains having a shape close to sech² shape can be generated just with sinusoidal modulation, without ultra-short driving pulses and ultra-broad bandwidth of the modulator. The pulse width and the repetition rate can be varied by changing the electrical driving conditions. Quasi-transform-limited optical pulseswith time-bandwidth product of 0.32 were successfully generated by the sinusoidally driven InGaAsP electroabsorption modulator with up to 20 GHz repetition rate. An application of a λ/4-shifted DFB laser-electroabsorption modulator integrated light source to a single-chip soliton source is also described. The high quality of the modulator-generator pulses has been proven by long-distance soliton transmission over 6400 km at 2.5 Gb/s using a recirculating fiber loop.     

Analysis of femtosecond optical pulse propagation in one-dimensional nonlinear photonic crystals using finite-difference time-domain method

In this paper, we have used the finite-difference time-domain (FDTD) method to analyze the optical pulse propagation in a nonlinear, one-dimensional photonic crystal (1DPC). Hyperbolic secant pulses with various carrier wavelengths are utilized in this study. In a nonlinear regime, a 1DPC introduces a photonic band-gap whose central wavelength and width depend on the input pulse intensity. In the present work, three different cases are considered. These correspond to the carrier wavelengths of the incident pulses being out of, near to, and partially in the band-gap. For each case, the effect of nonlinearity on pulse propagation is investigated. Also, we have analyzed the two-frequency regime, in which each of the two pulses has a different carrier frequency (wavelength). This kind of study can be done directly with FDTD without any further computational burden but it is somewhat complicated using nonlinear coupled-mode equations (NLCME) and nonlinear Schrödinger equation (NLSE), which require separate treatments for each carrier wavelength.     

Chirped optical pulse propagation in saturating nonlinear media

Using a variational method, we have investigated the propagation characteristics of a chirped optical pulse in anomalously dispersive media possessing saturating nonlinearity. For the special case of uniform loss less media, the dynamics of the temporal width of the pulse is shown to be equivalent to an oscillator of unit mass which is executing its motion under some effective potential well. The potential is examined and four different types of behavior of the pulse width are noticed. The role of saturation parameter and the initial chirp in determining the propagation characteristics have been examined. It is found that, both high value of chirp and saturation are detrimental to stable pulse propagation. Particularly, the effect of chirp becomes severe with the increase in the value of saturation. We have shown that incorporation of saturation in the nonlinearity leads to the existence of bistable soliton. For the case of a lossy medium, net broadening of width takes place over many cycles of oscillation. The net broadening decreases with the increase in the value of saturation.     

Theory of nonlinear directional couplers

A method is proposed for obtaining exact analytical solutions for the system of nonlinear equations for the propagation of electromagnetic waves in directional couplers with an arbitrary nonlinearity in the propagation constant. The resulting solutions can be used to determine the operating characteristics of nonlinear directional couplers. Zh. Tekh. Fiz. 69, 69–71 (August 1999)     

Optical limiting and pulse reshaping of picosecond pulse trains by fullerene C60

We present a dynamical theory of nonlinear absorption and propagation of a laser pulse train that contains 20 subpulses with an individual pulse width of 100 ps. It is shown that the accumulative nonlinearity and the reverse saturation absorption play important roles in the optical limiting performance and pulse shaping. When the incident field is not too strong, the population transfer reveals a slow response process, and the periodic sequence of short light pulses can be regarded as a continuous long pulse. The general theory is applied to fullerence C₆₀, which is a popular reverse saturable absorption material and a good limiter because of its larger excited-state absorption cross-section compared with that of the ground state. The propagation of the front subpulses is mainly affected by the linear transition between the ground state and the first excited singlet state, while the latter subpulses are attenuated by the excited-state absorption. Moreover, these two different kinds of absorption mechanisms result in different radial distributions for different subpulses. The pulse propagation is studied by solving numerically the coupled rate equations and the propagation equation of the optical pulse intensity, using experimental parameters as input. We suggest a new method to measure the lifetime of the triplet state.     

Spatiotemporal optical solitons in planar waveguide with periodically modulated cubic-quintic nonlinearity

The propagation and stability of spatiotemporal optical solitons (or optical bullets) in a planar waveguide with periodically modulated cubic-quintic nonlinearity is studied numerically as a function of the amplitudes of modulation (A _m ), the frequency of modulation (ω _m ) and the propagation distance z. The optical spatiotemporal solitons are the result of the balance between the nonlinear parameters, of dispersion (dispersion length, L _D ) and diffraction (diffraction length, L _d ) with temporal and spatial auto-focusing behavior respectively. With the objective of ensure the stability and preventing the collapse or the spreading of pulses, in this study we explore the cubic-quintic nonlinearity with the optical fields coupled by XPM and take into account several values for the non linear parameter α and for amplitudes (A _m ) and frequency (ω _m ) of modulation as a function of the propagation distance z and we cause the collisions of two pulses (envelope of the optical field) to ensure that the optical pulse are solitons. After numerical analysis of parameter settings selected four conditions and for all we get stable solitons and this paper shown that, for a fixed amplitude and frequency of modulation we have stable spatiotemporal solitons.     

五阶非线性光纤中连续谱相位扰动下的光传输与脉冲串产生

根据包含五阶非线性的扩展非线性薛定谔方程,数值研究了高斯型连续谱相位扰动而不是传统单色扰动下基于调制不稳定性的高重复率脉冲串产生.结果表明:脉冲串也能像传统情形那样形成,但却呈现出不同的特性.如脉冲数目有限,且各脉冲的高度、强度及间距不等.脉冲数目随传输距离增加而增加.而五阶非线性能使脉冲宽度和间距变小因而有利于高重复率脉冲串产生,负五阶非线性则相反.对脉冲串形成过程中演变啁啾的数值计算表明,啁啾及其随距离的变化都是高度非单调的,五阶非线性将改变啁啾的范围和量值.     

Nonlinearity management and diffraction management for the stabilization of two-dimensional spatial solitons

The nonlinear Schrödinger equation which governs the dynamics of two-dimensional spatial solitons in Kerr media with periodically varying diffraction and nonlinearity has been analyzed in this paper using variational approach and numerical studies. Analytical expressions for soliton parameters have been derived using variational analysis. Variational equations and partial differential equation have been simulated numerically. Analytical and numerical studies have shown that nonlinearity management and diffraction management stabilize the pulse against decay or collapse providing undisturbed propagation even for larger energies of the incident beam.     

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

We investigated the soliton solution for N$N$ coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons, study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management.     

Effect of laser beam induced nonlinearity on the performance of crystalline lens

This paper presents the performance of the human crystalline lens having gradient index (GRIN) structure in the presence of a moderate power laser pulse. Nonlinear dynamical equations have been set-up governing the laser pulse propagation in the lens by taking into account the nonlinearity introduced by the laser pulse. Semi-analytical results have been obtained by using the paraxial ray approximation when GRIN and nonlinearity effects are simultaneously present. Performance of the lens has been analyzed in two explicit cases. In the first case, only the GRIN structure is considered while in the second case the nonlinearity and the GRIN both are considered. A moderate power laser pulse can be used for self-focusing in the crystalline lens when GRIN effects alone are not sufficient to focus the laser pulse in the crystalline lens.     

Thirring combo-solitons with cubic nonlinearity and spatio-temporal dispersion

Abstract

The vector-coupled nonlinear Schrödinger equation, which can be applied to describe the propagation of Thirring optical solitons in birefringent ?bers with Kerr law nonlinearity, detuning, intermodal dispersion and spatiotemporal dispersion, has been studied analytically. By means of the complex envelope function ansatz, exact Thirring bright-dark combosolitons are reported, and the properties of these solitons are discussed.     

Effects of initial frequency chirp on the linear propagation characteristics of the exponential optical pulse

In this paper, the linear propagation characteristics of the exponential optical pulse with initial linear and nonlinear frequency chirp are numerically studied in a single mode fibre for \be₂<0. It can be found that the temporal full width at half maximum and time-bandwidth product of exponential pulse monotonically increase with the increase of propagation distance and decrease with the increase of linear chirp C for C<0.5, go through an initial decreasing stage near \zeta=1, then increase with the increase of propagation distance and linear chirp C for C\geq0.5. The broadening of pulses with negative chirp is faster than that with positive chirp. The exponential pulse with linear chirp gradually evolves into a near-Gaussian pulse. The effect of nonlinear chirp on waveform of the pulse is much greater than that of linear chirp. The temporal waveform breaking of exponential pulse with nonlinear chirp is first observed in linear propagation. Furthermore, the expressions of the spectral width and time-bandwidth product of the exponential optical pulse with the frequency chirp are given by use of the numerical analysis method.     

原子的共振激发—速率方程与半经典理论的比较

本文由半经典理论推得了原子电离率随脉冲空间传输出现周期性起伏这一新的相干作用结果,这点与速率方程的预计相差甚远.文中定量说明了利用速率方程对同位素分离过程进行分析时产生的系统误差,为实验分析工作提供了依据.     

Ultraslow solitons due to large quintic nonlinearity in coupled quantum well structures driven by two control laser beams

In this paper, we have shown the existence of large amounts of quintic nonlinearity in asymmetric three-coupled quantum wells, which arise due to a probe pulse and two controlling laser beams. The possibilities of generation and propagation of ultraslow bright optical solitons in these systems have been examined in situations of both Kerr and quintic nonlinearities. We have also demonstrated numerically that these solitons are stable. The modulation instability of a continuous or quasi-continuous wave probe beam has been also investigated and the role of quintic nonlinearity in suppressing this instability has been addressed.     

Higher-order effects on self-similar parabolic pulse in the microstructured fibre amplifier

By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows that the self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.